Fast mixing for attractors with a mostly contracting central direction

Abstract

Bonatti and Viana introduced a robust (non-empty interior) class of partially hyperbolic attractors of C²-diffeomorphisms on a compact manifold, for which they construct Sinai–Ruelle–Bowen measures. For some such robust examples, we prove the exponential decay of correlations and the central limit theorem, in the space of Hölder continuous functions. For the proof, we adapt the techniques (backward inducing, redundancy elimination algorithm) we have previously developed.